The function graphed above is:
Increasing on the interval(s)
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Decreasing on the interval(s)
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retirEEd retirEEd · Answer 1 · 2021-05-09T17:15:29+02:00

Step-by-step explanation:

When the slope of the function is positive, it is increasing

when the slope of the function is negative, it is decreasing

just like with the line function y = mx + b

so if you put a line tangent to the function at every point the slope of the line will indicate a increasing or decreasing point of the function

also beware where the slope is zero it is not increasing or decreasing

there are two intervals of increasing, one interval of decreasing and two point of zero slope or neither increasing or decreasing

increasing interval 1) x < -2 2) x > 1.5

decreasing interval 1) -2 < x < 1.5

at -2 and 1.5 the slope is zero

eudora eudora · Answer 2 · 2021-08-31T20:51:45+02:00

If the slope of a function is positive at all the points of the curve in a interval, function will be increasing.

f'(x) > 0

If the slope of a function is negative at all the points of the curve in a interval,

function will be decreasing.

f'(x) < 0

As we can see from the graph slope of the curve is positive in the intervals (-∞, -2) and (1.5, ∞) and decreasing in the interval (-2, 1.5).

Therefore, function is increasing in the intervals → (-∞, -2) and (1.5, ∞).

And the function is decreasing in the interval → (-2, 1.5)

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